Experimental Mode-Pairing Quantum Key Distribution Surpassing the Repeaterless Bound

Quantum key distribution (QKD) provides information-theoretic security for communication. The mode-pairing (MP) protocol emerges as a promising solution for long-distance QKD by eliminating the need for a global phase reference while maintaining the repeaterlike rate-loss scaling. Recent implementations have demonstrated its potential, but they either rely on costly ultrastable lasers or struggle with phase fluctuations from commercial lasers, particularly over long distances. As a result, surpassing the repeaterless bound with a practical system remains a challenge. In this work, we demonstrate a practical high-performance MP-QKD system using commercial lasers. To address phase fluctuations, we propose a frequency-tracking scheme based on fast Fourier transformation, enabling us to extend the pairing length to <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>2</a:mn><a:mo>×</a:mo><a:msup><a:mn>10</a:mn><a:mn>5</a:mn></a:msup></a:math> pulses (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>160</c:mn><c:mtext> </c:mtext><c:mtext> </c:mtext><c:mi mathvariant="normal">μ</c:mi><c:mi mathvariant="normal">s</c:mi></c:mrow></c:math>). We propose a model to carefully analyze the phase noise and optimize the system parameters. Our system achieves an optimal secret key rate of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mn>47.8</g:mn><g:mtext> </g:mtext><g:mtext> </g:mtext><g:mi>bit</g:mi><g:mo>/</g:mo><g:mi mathvariant="normal">s</g:mi></g:mrow></g:math> over 403 km of standard fiber (76.5 dB loss), exceeding the repeaterless bound by a factor of 2.92. Furthermore, we compare MP-QKD and twin-field QKD under various practical conditions and clarify the distinct application scenarios of the two protocols. These results confirm the feasibility of MP-QKD using cost-effective commercial technologies, paving the way for scalable quantum communication networks.